On Itô’s Stochastic Integral Equations

DOI10.1137/1114042zbMath0281.60066OpenAlexW2066358447MaRDI QIDQ4766341

Nicolai V. Krylov

Publication date: 1969

Published in: Theory of Probability & Its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/1114042

Mathematics Subject Classification ID

Stochastic integral equations (60H20)

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On the regularization effect of space-time white noise on quasi-linear parabolic partial differential equations ⋮ The parametrix method for skew diffusions ⋮ On nondegenerate quasilinear stochastic partial differential equations ⋮ On the uniqueness of solution to a martingale problem associated with a degenerate Lévy's operator ⋮ A remark on one-dimensional controlled diffusion processes ⋮ Asymptotic behavior of homogeneous additive functionals of the solutions of Itô stochastic differential equations with nonregular dependence on parameter ⋮ Asymptotic behaviour and functional limit theorems for a time changed Wiener process ⋮ Central limit theorem for a system of Markovian particles with mean field interactions ⋮ Existence of strong solutions for Itô's stochastic equations via approximations ⋮ A Viscous Ergodic Problem with Unbounded and Measurable Ingredients, Part 1: HJB Equation ⋮ On Iteration Improvement for Averaged Expected Cost Control for One-Dimensional Ergodic Diffusions ⋮ Integral representation of martingales motivated by the problem of endogenous completeness in financial economics ⋮ On Poisson equations with a potential in the whole space for “ergodic” generators ⋮ Planar diffusions with rank-based characteristics and perturbed Tanaka equations ⋮ On stochastic optimal control laws ⋮ Existence and uniqueness results for semilinear stochastic partial differential equations ⋮ Generalized volatility-stabilized processes ⋮ Existence of an endogenously complete equilibrium driven by a diffusion ⋮ Drift parameter estimation in stochastic differential equation with multiplicative stochastic volatility ⋮ Stochastic equations and krylov's estimates for semimartingales ⋮ A decomposition of additive functionals of finite energy ⋮ Méthodes de contrôle optimal en analyse complexe. I: Résolution d'équation de Monge Ampère ⋮ Weak convergence of integral functionals constructed from solutions of Itô’s stochastic differential equations with non-regular dependence on a parameter ⋮ Strong rate of convergence for the Euler-Maruyama approximation of stochastic differential equations with irregular coefficients ⋮ On weak uniqueness for some degenerate SDEs by global \(L^p\) estimates ⋮ Méthode de contrôle optimal en analyse complexe ou réelle. III. Diffusion des fonctions plurisousharmoniques ou convexes ⋮ On polynomial mixing bounds for stochastic differential equations ⋮ Reconstructing the drift of a diffusion from partially observed transition probabilities ⋮ Existence and uniqueness theorems for solutions of McKean–Vlasov stochastic equations ⋮ Nonexplosion and pathwise uniqueness of stochastic differential equation driven by continuous semimartingale with non-Lipschitz coefficients ⋮ Existence of strong solutions for Itô's stochastic equations via approximations: revisited ⋮ On diffusion approximation with discountinuous coefficients. ⋮ On the martingale problem associated with nondegenerate Lévy operators

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