Boundary non-crossings of Brownian pillow

On the average number of sharp crossings of certain Gaussian random polynomials

Heat and mass transfer of nanofluid over a linear stretching surface with Viscous dissipation effect

Boundary Layer Flow past a stretching surface with constant wall temperature, of a nanofluid is studied for heat transfer characteristics. The system of partial differential equations describing such a flow is subjected to similarity transformations gives rise to a boundary value problem involving a system of ordinary differential equations. This system is solved by a shooting method. Effect of...

Boundary Crossing Probabilities for Stationary Gaussian Processes and Brownian Motion1

Let X(t) be a stationary Gaussian process, /(/) a continuous function, and T a finite or infinite interval. This paper develops asymptotic estimates for P(X(t) > fit), some /er) when this probability is small. After transformation to an Ornstein Uhlenbeck process the results are also applicable to Brownian motion. In that special case, if W(t) is Brownian motion, / is continuously differentiabl...

Effect of magnetic field on the boundary layer flow, heat, and mass transfer of nanofluids over a stretching cylinder

The effect of a transverse magnetic field on the boundary layer flow and heat transfer of anisothermal stretching cylinder is analyzed. The governing partial differential equations for themagnetohydrodynamic, temperature, and concentration boundary layers are transformed into a setof ordinary differential equations using similarity transformations. The obtained ordinarydifferential equations ar...

On the Average Number of Sharp Crossings of Certain Gaussian Random Polynomials

Let Qn(x) = ∑n i=0 Aix i be a random algebraic polynomial where the coefficients A0, A1, · · · form a sequence of centered Gaussian random variables. Moreover, assume that the increments ∆j = Aj−Aj−1, j = 0, 1, 2, · · · are independent, assuming A−1 = 0. The coefficients can be considered as n consecutive observations of a Brownian motion. We obtain the asymptotic behaviour of the expected numb...