Brownian motion of multidimensional systems in nonpotential velocity-dependent fields of force

Penalisations of multidimensional Brownian motion, VI

control of the optical properties of nanoparticles by laser fields

در این پایان نامه، درهمتنیدگی بین یک سیستم نقطه کوانتومی دوگانه(مولکول نقطه کوانتومی) و میدان مورد مطالعه قرار گرفته است. از آنتروپی ون نیومن به عنوان ابزاری برای بررسی درهمتنیدگی بین اتم و میدان استفاده شده و تاثیر پارامترهای مختلف، نظیر تونل زنی(که توسط تغییر ولتاژ ایجاد می شود)، شدت میدان و نسبت دو گسیل خودبخودی بر رفتار درجه درهمتنیدگی سیستم بررسی شده اشت.با تغییر هر یک از این پارامترها، در...

Is the Driving Force of a Continuous Process a Brownian Motion or Fractional Brownian Motion?

Itô’s semimartingale driven by a Brownian motion is typically used in modeling the asset prices, interest rates and exchange rates, and so on. However, the assumption of Brownian motion as a driving force of the underlying asset price processes is rarely contested in practice. This naturally raises the question of whether this assumption is really appropriate. In the paper we propose a statisti...

Coupling all the Lévy stochastic areas of multidimensional Brownian motion

It is shown how to construct a successful co-adapted coupling of two copies of an n-dimensional Brownian motion (B1, . . . ,Bn) while simultaneously coupling all corresponding copies of Lévy stochastic areas ∫ Bi dBj − ∫ Bj dBi. It is conjectured that successful coadapted couplings still exist when the Lévy stochastic areas are replaced by a finite set of multiply iterated pathand time-integral...

Ergodic Properties of Multidimensional Brownian Motion with Rebirth

In a bounded open region of the d dimensional space we consider a Brownian motion which is reborn at a fixed interior point as soon as it reaches the boundary. The evolution is invariant with respect to a density equal, modulo a constant, to the Green function of the Dirichlet Laplacian centered at the point of return. We calculate the resolvent in closed form, study its spectral properties and...