اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدExistence of strong solutions for It^os stochastic equations via approximations. Revisited
105
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Given strong uniqueness for an It^os stochastic equation, we prove that its solution can beconstructed on any probability space by using, for example, Eulers polygonal approximations. Stochastic equations in $mathbb{R}^{d}$ and in domains in $mathbb{R}^{d}$ are considered. This is almost a copy of an old article in which we correct errors in the original proof of Lemma 4.1 found by Martin Dieckmann in 2013. We present also a new result on the convergence of tamed Euler approximations for SDEs with locally unbounded drifts, which we achieve by proving an estimate for appropriate exponential moments.
قيم البحث
اقرأ أيضاً
We consider It^o uniformly nondegenerate equations with time independent coefficients, the diffusion coefficient in $W^{1}_{d,loc}$, and the drift in $L_{d}$. We prove the unique strong solvability for any starting point and prove that as a function
of the starting point the solutions are Holder continuous with any exponent $<1$. We also prove that if we are given a sequence of coefficients converging in an appropriate sense to the original ones, then the solutions of approximating equations converge to the solution of the original one.
We propose to study a new type of Backward stochastic differential equations driven by a family of It^os processes. We prove existence and uniqueness of the solution, and investigate stability and comparison theorem.
A peculiar feature of It^os calculus is that it is an integral calculus that gives no explicit derivative with a systematic differentiation theory counterpart, as in elementary calculus. So, can we define a pathwise stochastic derivative of semimarti
ngales with respect to Brownian motion that leads to a differentiation theory counterpart to It^os integral calculus? From It^os definition of his integral, such a derivative must be based on the quadratic covariation process. We give such a derivative in this note and we show that it leads to a fundamental theorem of stochastic calculus, a generalized stochastic chain rule that includes the case of convex functions acting on continuous semimartingales, and the stochastic mean value and Rolles theorems. In addition, it interacts with basic algebraic operations on semimartingales similarly to the way the deterministic derivative does on deterministic functions, making it natural for computations. Such a differentiation theory leads to many interesting applications some of which we address in an upcoming article.
We prove It^os formula for the $L_{p}$-norm of a stochastic $W^{1}_{p}$-valued processes appearing in the theory of SPDEs in divergence form.
This paper establishes It^os formula along a flow of probability measures associated with gene-ral semimartingales. This generalizes existing results for flow of measures on It^o processes. Our approach is to first prove It^os formula for cylindrical
polynomials and then use function approximation and localization techniques for the general case. This general form of It^os formula enables derivation of dynamic programming equations and verification theorems for McKean-Vlasov controls with jump diffusions and for McKean-Vlasov mixed regular-singular control problems. It also allows for generalizing the classical relation between the maximum principle and the dynamic programming principle to the McKean-Vlasov singular control setting, where the adjoint process is expressed in term of the derivative of the value function with respect to probability measures.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
