اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدOn one-dimensional stochastic differential equations involving the maximum process
268
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We prove existence and pathwise uniqueness results for four different types of stochastic differential equations (SDEs) perturbed by the past maximum process and/or the local time at zero. Along the first three studies, the coefficients are no longer Lipschitz. The first type is the equation label{eq1} X_{t}=int_{0}^{t}sigma (s,X_{s})dW_{s}+int_{0}^{t}b(s,X_{s})ds+alpha max_{0leq sleq t}X_{s}. The second type is the equation label{eq2} {l} X_{t} =ig{0}{t}sigma (s,X_{s})dW_{s}+ig{0}{t}b(s,X_{s})ds+alpha max_{0leq sleq t}X_{s},,+L_{t}^{0}, X_{t} geq 0, forall tgeq 0. The third type is the equation label{eq3} X_{t}=x+W_{t}+int_{0}^{t}b(X_{s},max_{0leq uleq s}X_{u})ds. We end the paper by establishing the existence of strong solution and pathwise uniqueness, under Lipschitz condition, for the SDE label{e2} X_t=xi+int_0^t si(s,X_s)dW_s +int_0^t b(s,X_s)ds +almax_{0leq sleq t}X_s +be min_{0leq s leq t}X_s.
قيم البحث
اقرأ أيضاً
In this paper we study time-inhomogeneo
In this paper, we deal with a class of reflected backward stochastic differential equations associated to the subdifferential operator of a lower semi-continuous convex function driven by Teugels martingales associated with L{e}vy process. We obtain
the existence and uniqueness of solutions to these equations by means of the penalization method. As its application, we give a probabilistic interpretation for the solutions of a class of partial differential-integral inclusions.
In this paper we solve real-valued rough differential equations (RDEs) reflected on an irregular boundary. The solution $Y$ is constructed as the limit of a sequence $(Y^n)_{ninmathbb{N}}$ of solutions to RDEs with unbounded drifts $(psi_n)_{ninmathb
b{N}}$. The penalisation $psi_n$ increases with $n$. Along the way, we thus also provide an existence theorem and a Doss-Sussmann representation for RDEs with a drift growing at most linearly. In addition, a speed of convergence of the sequence of penalised paths to the reflected solution is obtained. We finally use the penalisation method to prove that the law at time $t>0$ of some reflected Gaussian RDE is absolutely contiuous with respect to the Lebesgue measure.
In this short note we will provide a sufficient and necessary condition to have uniqueness of the location of the maximum of a stochastic process over an interval. The result will also express the mean value of the location in terms of the derivative
of the expectation of the maximum of a linear perturbation of the underlying process. As an application, we will consider a Brownian motion with variable drift. The ideas behind the method of proof will also be useful to study the location of the maximum, over the real line, of a two-sided Brownian motion minus a parabola and of a stationary process minus a parabola.
The paper is concerned with adapted solution of a multi-dimensional BSDE with a diagonally quadratic generator, the quadratic part of whose $i$th component only depends on the $i$th row of the second unknown variable. Local and global solutions are g
iven. In our proofs, it is natural and crucial to apply both John-Nirenberg and reverse Holder inequalities for BMO martingales.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
