Mark Freidlin
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Russian-American probability theorist
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Mark Freidlinmathematics Degrees
Mathematics
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#5557
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Probability Theory
#53
World Rank
#74
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#16
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Measure Theory
#1237
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#1568
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#450
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Mathematics
Mark Freidlin's Degrees
- PhD Mathematics Moscow State University
Why Is Mark Freidlin Influential?
(Suggest an Edit or Addition)According to Wikipedia, Mark Iosifovich Freidlin is a Russian-American probability theorist who works as a Distinguished University Professor of Mathematics at the University of Maryland, College Park. He is one of the namesakes of the Freidlin–Wentzell theory, which is an important part of the large deviations theory. Freidlin and Wentzell are the authors of the first monograph on the large deviations theory for stochastic processes . The Freidlin-Wentzell theory describes, in particular, the long-time effects caused by random perturbations. The latest edition of the book was published by Springer in 2012. It contains not just the results on large deviations but also new results on other asymptotic problems, in particular, on the averaging principle for stochastic perturbations. Other works of Mark Freidlin concern perturbations of Hamiltonian systems, wave front propagation in reaction-diffusion equations, non-linear perturbations of partial differential equations. stochasticity in deterministic dynamical systems.
Mark Freidlin's Published Works
Number of citations in a given year to any of this author's works
Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author
Published Works
- Random Perturbations of Dynamical Systems (1984) (4221)
- Functional Integration And Partial Differential Equations (1985) (870)
- ON SMALL RANDOM PERTURBATIONS OF DYNAMICAL SYSTEMS (1970) (398)
- Functional Integration and Partial Differential Equations. (AM-109), Volume 109 (1985) (287)
- Diffusion Processes on Graphs and the Averaging Principle (1993) (214)
- Averaging principle for a class of stochastic reaction–diffusion equations (2008) (159)
- Random perturbations of Hamiltonian systems (1994) (146)
- Some Remarks on the Smoluchowski–Kramers Approximation (2004) (121)
- Limit Theorems for Large Deviations and Reaction-Diffusion Equations (1985) (117)
- Markov Processes and Di+erential Equations: Asymptotic Problems (1996) (114)
- Random perturbations of reaction-difiusion equations: the quasi de-terministic approximation (1988) (104)
- THE AVERAGING PRINCIPLE AND THEOREMS ON LARGE DEVIATIONS (1978) (94)
- Diffusion processes on graphs: stochastic differential equations, large deviation principle (2000) (93)
- A comparison of homogenization and large deviations, with applications to wavefront propagation (1999) (69)
- Random perturbations of nonlinear oscillators (1998) (65)
- On Stable Oscillations and Equilibriums Induced by Small Noise (2001) (63)
- On the Smoluchowski-Kramers approximation for a system with an infinite number of degrees of freedom (2006) (62)
- Dirichlet’s Problem for an Equation with Periodic Coefficients Depending on a Small Parameter (1964) (61)
- Random perturbations of dynamical systems and diffusion processes with conservation laws (2004) (61)
- Geometric optics approach to reaction-diffusion equations (1986) (52)
- Diffusion processes on an open book and the averaging principle (2004) (48)
- Smoluchowski-Kramers approximation for a general class of SPDEs (2006) (47)
- Long-Time Behavior of Weakly Coupled Oscillators (2006) (43)
- On stochastic behavior of perturbed Hamiltonian systems (2000) (41)
- On the Factorization of Non-Negative Definite Matrices (1968) (41)
- Some Problems Concerning Stability under Small Random Perturbations (1973) (40)
- Fast oscillating random perturbations of dynamical systems with conservation laws (1995) (36)
- Smoluchowski–Kramers approximation in the case of variable friction (2011) (35)
- SMOLUCHOWSKI-KRAMERS APPROXIMATION AND EXIT PROBLEMS (2005) (35)
- Averaging Principle for Stochastic Perturbations of Multifrequency Systems (2003) (33)
- Wave Front Propagation for KPP-Type Equations (1995) (33)
- Gaussian Perturbations of Dynamical Systems. Neighborhood of an Equilibrium Point (1998) (33)
- APPROXIMATION OF QUASI-POTENTIALS AND EXIT PROBLEMS FOR MULTIDIMENSIONAL RDE'S WITH NOISE (2011) (32)
- On random perturbations of Hamiltonian systems with many degrees of freedom (2001) (31)
- On the dirichlet problem for a class of second order pde systems with small parameter (1990) (30)
- Coupled Reaction-Diffusion Equations (1991) (30)
- Reaction-Diffusion in Incompressible Fluid: Asymptotic Problems (2002) (30)
- Reaction-Diffusion Equations with Randomly Perturbed Boundary Conditions (1992) (28)
- Semi-linear pde's and limit theorems for large deviations (1992) (28)
- A REMARK ON RANDOM PERTURBATIONS OF THE NONLINEAR PENDULUM (1999) (27)
- Markov processes and differential equations (1996) (26)
- Quasipotential and exit time for 2D Stochastic Navier-Stokes equations driven by space time white noise (2014) (26)
- ON STOCHASTIC PERTURBATIONS OF DYNAMICAL SYSTEMS WITH FAST AND SLOW COMPONENTS (2001) (26)
- Quasilinear parabolic equations and measures in function space (1967) (24)
- On metastable regimes in stochastic Lamb system (2006) (23)
- Small Mass Asymptotics for a Charged Particle in a Magnetic Field and Long-Time Influence of Small Perturbations (2011) (22)
- Necessary and Sufficient Conditions for Weak Convergence of One-Dimensional Markov Processes (1994) (21)
- The Multidimensional Case (2012) (20)
- Nonlinear stochastic perturbations of dynamical systems and quasi-linear parabolic PDE’s with a small parameter (2009) (19)
- Large Deviations for Markov Processes Corresponding to PDE Systems (1993) (18)
- ON THE SMOOTHNESS OF SOLUTIONS OF DEGENERATE ELLIPTIC EQUATIONS (1968) (18)
- Large Deviations for the Langevin Equation with Strong Damping (2015) (17)
- The Action Functional for a Class of Stochastic Processes (1973) (17)
- On the Smoluchowski-Kramers approximation for SPDEs and its interplay with large deviations and long time behavior (2016) (16)
- Diffusion Processes with Reflection and Problems with a Directional Derivative on a Manifold with a Boundary (1963) (15)
- Small mass asymptotic for the motion with vanishing friction (2012) (15)
- On Perturbations of Generalized Landau-Lifshitz Dynamics (2011) (13)
- Metastable Distributions of Markov Chains with Rare Transitions (2016) (13)
- On a Stochastic Model for Moisture Budget in an Eulerian Atmospheric Column (1997) (12)
- On the Neumann problem for PDE’s with a small parameter and the corresponding diffusion processes (2012) (12)
- On the behavior of diffusion processes with traps (2015) (12)
- On Stochastic Perturbations of Dynamical Systems with a “Rough” Symmetry. Hierarchy of Markov Chains. (2014) (12)
- Fast transport asymptotics for stochastic RDEs with boundary noise (2010) (12)
- Optimal Residence Time Control of Hamiltonian Systems Perturbed by White Noise (1998) (11)
- Wave front propagation and large deviations for diffusion –transmutation process (1996) (11)
- Deterministic and stochastic perturbations of area preserving flows on a two-dimensional torus (2011) (10)
- Metastability for nonlinear random perturbations of dynamical systems (2009) (10)
- On Diffusion in Narrow Random Channels (2012) (10)
- Reaction-diffusion equations with nonlinear boundary conditions in narrow domains (2010) (10)
- Averaging principle for perturbed random evolution equations and corresponding Dirichlet problems (1993) (8)
- On the Structure of the Infinitesimal $\sigma $-Algebra of a Gaussian Process (1962) (8)
- Large Deviations at Saint-Flour (2012) (7)
- The Averaging Principle. Fluctuations in Dynamical Systems with Averaging (1998) (7)
- The Dynkin festschrift : Markov processes and their applications (1994) (7)
- ON STOCHASTICITY OF SOLUTIONS OF DIFFERENTIAL EQUATIONS WITH A SMALL DELAY (2005) (7)
- A threshold estimation problem for processes with hysteresis (1998) (7)
- On wave fronts propagation in multicomponent media (1983) (7)
- Probabilistic approach to the small viscosity asymptotics for Navier-Stokes equations (1997) (7)
- Hysteresis in randomly perturbed fast dynamical systems (2001) (6)
- Fast flow asymptotics for stochastic incompressible viscous fluids in R 2 and SPDEs on graphs (2016) (6)
- The Exterior Dirichlet Problem in the Class of Bounded Functions (1966) (6)
- Some Recent Results on Averaging Principle (2008) (6)
- Diffusion Processes and PDE’s in Narrow Branching Tubes (1996) (5)
- SPDEs on narrow domains and on graphs: an asymptotic approach (2014) (5)
- Non-standard analysis and singular perturbations of ordinary differential equations (2016) (5)
- ON STOCHASTICITY IN NEARLY-ELASTIC SYSTEMS (2012) (5)
- METASTABILITY FOR RANDOM PERTURBATIONS OF NEARLY-HAMILTONIAN SYSTEMS (2008) (5)
- Long Time Influence of Small Perturbations and Motion on the Simplex of Invariant Probability Measures (2020) (5)
- On Second Order Elliptic Equations with a Small Parameter (2012) (5)
- Large deviation principle for the diffusion-transmutation processes and dirichlet problem for PDE systems with small parameter (1996) (4)
- Wave front propagation for a reaction–diffusion equation in narrow random channels (2013) (4)
- Deterministic 3D-Perturbations of Planar Incompressible Flow Lead to Stochasticity (2003) (4)
- Surveys in Applied Mathematics (1995) (4)
- Perturbations of the Motion of a Charged Particle in a Noisy Magnetic Field (2012) (4)
- Tunneling Soliton in the Equations of Reaction‐Diffusion Type (1987) (4)
- AVERAGING PRINCIPLE FOR QUASI-LINEAR PARABOLIC PDEs AND RELATED DIFFUSION PROCESSES (2012) (3)
- EXISTENCE "IN THE LARGE" OF SMOOTH SOLUTIONS OF DEGENERATE QUASILINEAR EQUATIONS (1969) (3)
- Central limit theorem results for a reaction-diffusion equation with fast-oscillating boundary perturbations (1992) (3)
- On diffusions in media with pockets of large diffusivity (2017) (3)
- Erratum to: “On wave fronts propagation in multicomponent media” [Trans. Amer. Math. Soc. 276 (1983), no. 1, 181–191; MR0684501 (84a:35027)] (1985) (3)
- On Small (in the Weak Sense) Perturbations in the Coefficients of a Diffusion Process (1967) (3)
- Fast flow asymptotics for stochastic incompressible viscous fluids in $$\mathbb {R}^2$$R2 and SPDEs on graphs (2016) (3)
- Modeling of temperature-dependent hysteresis within the framework of dynamical systems (2002) (3)
- Stabilization of solutions of certain parabolic equations and systems (1968) (3)
- Correction to “Random perturbations of dynamical systems and diffusion processes with conservation laws” (2006) (3)
- Reaction-Convection in Incompressible 3D-Fluid: A Homogenization Problem (2006) (2)
- Stability of highly reliable systems (1976) (2)
- Front Propagation for Reaction–Diffusion Equations in Composite Structures (2018) (2)
- Diffusion Approximation for Noise-Induced Evolution of First Integrals in Multifrequency Systems (2020) (2)
- Thermostat-Like Perturbations of an Oscillator (2016) (2)
- Autonomous Stochastic Perturbations of Dynamical Systems (2003) (2)
- A Note on the Generalized Solution of the Dirichlet Problem (1965) (2)
- On Degenerating Elliptic Equations (1969) (2)
- Noise Sensitivity of Stochastic Resonance and Other Problems Related to Large Deviations (2003) (2)
- Perturbations Leading to Markov Processes (1998) (1)
- On the motion of light particles perturbed by noise (2000) (1)
- ON LOGARITHMIC ASYMPTOTICS OF STOCHASTIC RESONANCE FREQUENCIES (2003) (1)
- Origin of the universality of long-time thermal relaxations in hysteretic systems (2000) (1)
- Wave front propagation in semi-linear differential equations and systems of KPP-type (1992) (1)
- Averaging Principle: Continuation (1996) (1)
- Remarks and Generalizations (1996) (1)
- [Asymptotic analysis of the functioning of a multienzyme complex performing electron transfer]. (1979) (1)
- Small Random Perturbations on a Finite Time Interval (1998) (1)
- The spectral method and ergodic theorems for general Markov chains (2016) (1)
- Diffusion in the Presence of Cells with Semi-permeable Membranes (2019) (1)
- Communications of the Moscow Mathematical Society: Degenerate Diffusion Processes and Differential Equations with a Small Parameter (1978) (1)
- A model discrimination method for processes with different memory structure (1999) (1)
- Large deviations, stochastic resonance, and hysteresis☆ (2001) (1)
- Autonomous random perturbations of dynamical systems (2002) (1)
- VII. WAVE FRONT PROPAGATION IN PERIODIC AND RANDOM MEDIA (1985) (0)
- Markov Perturbations on Large Time Intervals (1998) (0)
- PDE's, Random Processes and Fields: Asymptotic Problems. (1995) (0)
- Small Parameter in Higher Derivatives: Levinson’s Case (1996) (0)
- Mark Freidlin Interview May 22, 1987 (1987) (0)
- [Kinetics and thermodynamics of electron transport reactions in carrier molecule complexes during photosynthesis. Approximation method]. (1979) (0)
- On Diffusion in Narrow Random Channels (2013) (0)
- Mark Freidlin Interview July 19, 1987 (1987) (0)
- Stability Under Random Perturbations (2012) (0)
- I. STOCHASTIC DIFFERENTIAL EQUATIONS AND RELATED TOPICS (1985) (0)
- Boris Rufimovich Vainberg (2019) (0)
- Large Scale Approximation for Reaction-Diffusion Equations (1996) (0)
- On the Long‐Time Behavior of the Solutions of Quasi‐Linear Parabolic Equations with Small Parameter (1985) (0)
- Sharpenings and Generalizations (1998) (0)
- Stabilization of Hamiltonian systems perturbed by white noise (1997) (0)
- V. QUASI-LINEAR PARABOLIC EQUATIONS WITH NON-NEGATIVE CHARACTERISTIC FORM (1985) (0)
- Erratum to "On Wave Fronts Propagation in Multicomponent Media" (1985) (0)
- The asymptotic behaviour of the solution of a hyperbolic system of equations with a non-linear (2016) (0)
- Quasipotential and exit time for 2D Stochastic Navier-Stokes equations driven by space time white noise (2014) (0)
- Random Perturbations of Dynamical Systems: Large Deviations and Averaging (1994) (0)
- Averaging Principle for Stochastic Processes and for Partial Differential Equations (1996) (0)
- Igor’ Vladimirovich Girsanov (1967) (0)
- Homogenization of diffusion processes in tubular domains (2007) (0)
- Wave Fronts in Slowly Changing Media (1996) (0)
- III. BOUNDARY VALUE PROBLEMS FOR EQUATIONS WITH NON-NEGATIVE CHARACTERISTIC FORM (1985) (0)
- COMMUNICATIONS OF THE MOSCOW MATHEMATICAL SOCIETY: On the motion of light particles perturbed by noise (2000) (0)
- Appeal for Moscow refuseniks (1982) (0)
- Wave Fronts in Reaction-Diffusion Equations (1996) (0)
- The Large Deviation Case (1996) (0)
- IV. SMALL PARAMETER IN SECOND-ORDER ELLIPTIC DIFFERENTIAL EQUATIONS (1985) (0)
- On stabilization of the solutions of parabolic equations with small parameter. (1984) (0)
- Probabilities of Large Deviations for Randomly Perturbed Dynamic Systems and Stochastic Stability (1974) (0)
- Voices from a wilderness (1981) (0)
- Autonomous stochastic perturbations of hamiltonian systems (2004) (0)
- VI. QUASI-LINEAR PARABOLIC EQUATIONS WITH SMALL PARAMETER. WAVE FRONTS PROPAGATION (1985) (0)
- II. REPRESENTATION OF SOLUTIONS OF DIFFERENTIAL EQUATIONS AS FUNCTIONAL INTEGRALS AND THE STATEMENT OF BOUNDARY V A LU E PROBLEMS (1985) (0)
- Boris R. Vainberg (on his 80th birthday) (2018) (0)
- Book reviews (1985) (0)
- Stochastic Processes Defined by ODE’s (1996) (0)
- Averaging in the case of multiple invariant measures for the fast system (2020) (0)
- Homogenization in PDE’s and in Stochastic Processes (1996) (0)
- LIST OF NOTATIONS (1985) (0)
- On the Neumann problem for PDE’s with a small parameter and the corresponding diffusion processes (2010) (0)
- Onstabilization ofthesolutions ofparabolic equations withsmall parameter (1984) (0)
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