1,720,990 research outputs found
Pathwise asymptotics for Volterra processes conditioned to a noisy version of the Brownian motion
Full text linkIn this paper we investigate a problem of large deviations for continuous Volterra processes under the influence of model disturbances. More precisely, we study the behavior, in the near future after T, of a Volterra process driven by a Brownian motion in a case where the Brownian motion is not directly observable, but only a noisy version is observed or some linear functionals of the noisy version are observed. Some examples are discussed in both cases
Some Large Deviations Principles for Time-Changed Gaussian Processes
No full textLetX= (X(t))(t >= 0)(X(0) = 0) be a continuous centered Gaussian process on a probability space (omega,F,P), and let (Y-t)(t is an element of)[0,1] (Y-0= 0) be a continuous process (on the same probability space) with nondecreasing paths, independent ofX. Define the time-changed Gaussian processZ(t)=X(Y-t),t is an element of [0,1]. In this paper, we investigate a problem of finite-dimensional large deviations and a problem of pathwise large deviations for time-changed continuous Gaussian processes. As applications, we considered subordinated Gaussian processes
Asymptotic results for finite superpositions of Ornstein–Uhlenbeck processes
Full text linkA model of intermittency based on superposition of Lévy driven
Ornstein–Uhlenbeck processes is studied in [6]. In particular, as shown
in Theorem 5.1 in that paper, finite superpositions obey a (sample path)
central limit theoremunder suitable hypotheses. In this paper we prove
large (and moderate) deviation results associated with this central limit
theorem
Pathwise asymptotics for Volterra type stochastic volatility models
No full textWe study stochastic volatility models in which the volatility process is a positive continuous function of a continuous Volterra stochastic process. We state some pathwise large deviation principles for the scaled log-price
Large deviations for perturbed Gaussian processes and logarithmic asymptotic estimates for some exit probabilities
No full textThe main results in this paper concern large deviations for families of
non-Gaussian processes obtained as suitable perturbations of continuous centered multivariate Gaussian processes which satisfy a large deviation principle. We present some corollaries and, as a consequence, we obtain logarithmic asymptotic estimates for exit probabilities from suitable halfspaces and quadrants
Asymptotics for multifactor Volterra type stochastic volatility models
No full textWe study multidimensional stochastic volatility models in which the volatility process is a positive continuous function of a continuous multidimensional Volterra process that can be not self-similar. The main results obtained in this paper are a generalization of the results due, in the one-dimensional case, to Cellupica and Pacchiarotti (J. Theor. Probab. 34(2):682-727). We state some (pathwise and finite-dimensional) large deviation principles for the scaled log-price and as a consequence some (pathwise and finite-dimensional) short-time large deviation principles
Large deviations for conditional Volterra processes
No full textIn this articlewe investigate a problem of large deviations for continuous
Gaussian Volterra processes, conditioned to follow a fixed trajectory up
to a fixed time T > 0, in order to establish the behavior of the process
in the near future after T and to give an asymptotic estimate of the exit
probability of its bridge. Some examples are considered
On large deviations for some sequences of weighted means of Gaussian processes
No full textIn this paper we study some sequences of weighted means of continuous real valued Gaussian processes. More precisely we consider suitable generalizations of both arithmetic and logarithmic means of a Gaussian process with covariance function which satisfies either an exponential decay condition or a power decay condition. Our aim is to provide limits of variances of functionals of such weighted means which allow the application of some large deviation results in the literature
Large deviations for a class of tempered subordinators and their inverse processes
No full textWe consider a class of tempered subordinators, namely a class of subordinators with
one-dimensional marginal tempered distributions which belong to a family studied in
[3]. The main contribution in this paper is a non-central moderate deviations result.
More precisely we mean a class of large deviation principles that fill the gap between
the (trivial) weak convergence of some non-Gaussian identically distributed random
variables to their common law, and the convergence of some other related random
variables to a constant. Some other minor results concern large deviations for the
inverse of the tempered subordinators considered in this paper; actually, in some
results, these inverse processes appear as random time-changes of other independent
processes
Large deviations for conditionally Gaussian processes: estimates of level crossing probability
Full text linkThe problem of (pathwise) large deviations for conditionally continuous Gaussian processes is investigated. The theory of large deviations for Gaussian processes is extended to the wider class of random processes – the conditionally Gaussian processes. The estimates of level crossing probability for such processes are given as an application
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