Related papers: On the dependence between a Wiener process and its…

Let us consider the process $(X_t^{(\alpha)})_{t\in[0,T)}$ given by the SDE $dX_t^{(\alpha)} = -\frac{\alpha}{T-t}X_t^{(\alpha)} dt+ dB_t$, $t\in[0,T)$, where $\alpha\in R$, $T\in(0,\infty)$, and $(B_t)_{t\geq 0}$ is a standard Wiener…

We develop quantum algorithms for pricing Asian and barrier options under the Heston model, a popular stochastic volatility model, and estimate their costs, in terms of T-count, T-depth and number of logical qubits, on instances under…

Using the Euler--Maruyama technique, we show that a class of Wiener processes exist that are obtained by computing an arbitrary positive power of them. This can be accomplished with a proper set of definitions that makes meaningful the…

In this paper, we consider a nonlinear filtering model with observations driven by correlated Wiener processes and point processes. We first derive a Zakai equation whose solution is a unnormalized probability density function of the filter…

We consider a method for the approximation of iterated stochastic integrals of arbitrary multiplicity $k$ $(k\in \mathbb{N})$ with respect to the infinite-dimensional $Q$-Wiener process using the mean-square approximation method of iterated…

Consider the Slepian process $S$ defined by $ S(t)=B(t+1)-B(t),t\in [0,1]$ with $B(t),t\in \R$ a standard Brownian motion.In this contribution we analyze the joint distribution between the maximum $m_{s}=\max_{0\leq u\leq s}S(u)$ certain…

We develop the general integral transforms (GIT) method for pricing barrier options in the time-dependent Heston model (also with a time-dependent barrier) where the option price is represented in a semi-analytical form as a two-dimensional…

Recently, a new class of second order Runge-Kutta methods for It\^o stochastic differential equations with a multidimensional Wiener process was introduced by R\"o{\ss}ler. In contrast to second order methods earlier proposed by other…

The paper deals with a generalization of the risk model with stochastic premiums where dependence structures between claim sizes and inter-claim times as well as premium sizes and inter-premium times are modeled by…

Let $W_i=\{W_i(t), t\in \mathbb{R}_+\}, i=1,2$ be two Wiener processes and $W_3=\{W_3(\mathbf{t}), \mathbf{t}\in \mathbb{R}_+^2\}$ be a two-parameter Brownian sheet, all three processes being mutually independent. We derive upper and lower…

The purpose of the article is twofold. Firstly, we review some recent results on the maximum likelihood estimation in the regression model of the form $X_t = \theta G(t) + B_t$, where $B$ is a Gaussian process, $G(t)$ is a known function,…

Quantum systems with variables in ${\mathbb Z}(d)$ are considered, and three different structures are studied. The first is weak mutually unbiased bases, for which the absolute value of the overlap of any two vectors in two different bases…

We study rates of convergence in central limit theorems for the partial sum of squares of general Gaussian sequences, using tools from analysis on Wiener space. No assumption of stationarity, asymptotically or otherwise, is made. The main…

In this paper, we consider a $d$-dimensional continuous It\^{o} process which is observed at $n$ regularly spaced times on a given time interval $[0,T]$. This process is driven by a multidimensional Wiener process and our aim is to provide…

We prove one-to-one correspondences between certain decreasing Loewner chains in the upper half-plane, a special class of real-valued Markov processes, and quantum stochastic processes with monotonically independent additive increments.…

In this study, we propose a new formula for spread option pricing with the dependence of two assets described by a copula function. The advantage of the proposed method is that it requires only the numerical evaluation of a one-dimensional…

We consider a system consisting of a planar random walk on a square lattice, submitted to stochastic elementary local deformations. Depending on the deformation transition rates, and specifically on a parameter $\eta$ which breaks the…

We consider a class of stochastic processes $X$ defined by $X\left( t\right) =\int_{0}^{T}G\left( t,s\right) dM\left( s\right) $ for $t\in\lbrack0,T]$, where $M$ is a square-integrable continuous martingale and $G$ is a deterministic…

This work deals with a system of interacting reinforced stochastic processes, where each process $X^j=(X_{n,j})_n$ is located at a vertex $j$ of a finite weighted direct graph, and it can be interpreted as the sequence of "actions" adopted…

The problem of optimal linear estimation of a linear functional depending on the unknown values of periodically correlated stochastic process from observations of the process with additive noise is considered. Formulas for calculating the…